Question

A car accelerates at 2.0 m/s2 for 10 seconds. The car has an initial velocity of 10 m/s. What is the final velocity of the vehicle?

Answer 1

Answer: The final velocity will be 30 m/s

Step-by-step explanation:

`v_(i) = 10 m/s\\a = 2.0m/s^(2) \\t = 10s\\v_(f) = ?\\\\a = (v_(f) - v_(i))/(t) \\2.0 = (v_(f) - 10)/(10) \\20 = v_(f) - 10\\v_(f) = 30`

Answer 2

30 m/s

Step-by-step explanation:

`\boxed{\begin{array}{c} \text{\underline{The Constant Acceleration Equations (SUVAT)}}\\\\\begin{aligned}v&=u+at\\\\s&=ut+(1)/(2)at^2\\\\ s&=\left((u+v)/(2)\right)t\\\\v^2&=u^2+2as\\\\s&=vt-(1)/(2)at^2\end{aligned}\end{array}}`

`\boxed{\begin{minipage}{9 cm}s = displacement in m (meters)\\u = initial velocity in m/s (meters per second)\\v = final velocity in m/s (meters per second)\\a = acceleration in m/s$^(2)$ (meters per second per second)\\t = time in s (seconds)\\\\When using SUVAT, assume the object is modeled\\ as a particle and that acceleration is constant.\end{minipage}}`

Given:

• u = 10 m/s
• v =
• a = 2.0 m/s²
• t = 10 s

Substitute the given values into v = u + at and solve for v:

`\begin{aligned}v & = u+at\\\implies v & = 10 + 2(10)\\& = 10 + 20\\& = 30\; \sf m/s\end{aligned}`

Therefore, the final velocity of the vehicle is 30 m/s.